Updated on 2024/04/30

写真a

 
LE GALL Francois Pierre Marcel
 
Organization
Graduate School of Mathematics Division of Mathematics Computational Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor
Contact information
メールアドレス
External link

Degree 1

  1. Phd (Computer Science) ( 2006.3   The University of Tokyo ) 

Research Interests 4

  1. Distributed computing

  2. Algorithms

  3. Computational complexity

  4. Quantum computing

Research Areas 1

  1. Informatics / Theory of informatics

Current Research Project and SDGs 4

  1. Distributed Computing

  2. Quantum computing

  3. Computational Complexity

  4. Algorithms

Research History 5

  1. Nagoya University   Graduate School of Mathematics   Professor

    2022.4

  2. Nagoya University   Graduate School of Mathematics   Associate professor

    2019.10 - 2022.3

  3. Kyoto University   Graduate School of Informatics   Designated associate professor

    2016.4 - 2019.9

  4. The University of Tokyo   Graduate School of Information Science and Technology   Designated associate professor

    2012.4 - 2016.3

  5. The University of Tokyo   Graduate School of Information Science and Technology   Designated lecturer

    2009.4 - 2012.3

Professional Memberships 5

  1. ACM SIGACT

  2. EATCS

  3. INFORMATION PROCESSING SOCIETY OF JAPAN

  4. ACM

  5. 日本数学会

Committee Memberships 14

  1.   Editorial board member  

    2023.1   

  2. Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC)   Steering committee member  

    2022.10   

  3. 26th Conference on Quantum Information Processing (QIP 2023)   Program committee chair  

    2022.5 - 2023.2   

  4. ACM Transactions on Quantum Computing   Editorial board member  

    2019.6   

  5. ACM Transactions on Quantum Computing   Editorial board member  

    2019.6   

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    Committee type:Academic society

  6. Computational Complexity   Editorial board member  

    2016.6   

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    Committee type:Academic society

  7. 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP 2024)   Program Committee member  

    2024.2 - 2024.7   

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    Committee type:Academic society

  8. ACM-SIAM Symposium on Discrete Algorithms (SODA24)   Program Committee member  

    2023.7 - 2024.1   

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    Committee type:Academic society

  9. 2023 Computational Complexity Conference (CCC 2023)   Program Committee member  

    2023.2 - 2023.7   

  10. Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC)   Steering committee member  

    2022.10   

  11. 26th Conference on Quantum Information Processing (QIP 2023)   Program committee chair  

    2022.5 - 2023.2   

  12. 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)   Program committee chair  

    2021.10 - 2022.7   

  13. 電子情報通信学会   コンピュテーション研究会専門委員  

    2016.6 - 2022.5   

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    Committee type:Academic society

  14. 51st EATCS International Colloquium on Automata, Languages and Programming   Program Committee member  

       

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    Committee type:Academic society

▼display all

Awards 2

  1. NISTEP Award 2017

    2017.11   MEXT  

    Francois Le Gall

  2. ISSAC 2014 Distinguished Paper Award

    2014.7   ACM-SIGAL  

 

Papers 44

  1. Faster Rectangular Matrix Multiplication by Combination Loss Analysis Reviewed

    François Le Gall

    Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)     page: 3765 - 3791   2024.1

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    Publishing type:Part of collection (book)   Publisher:Society for Industrial and Applied Mathematics  

    DOI: 10.1137/1.9781611977912.133

  2. Dequantizing the Quantum singular value transformation: hardness and applications to Quantum chemistry and the Quantum PCP conjecture. Reviewed

    Sevag Gharibian, François Le Gall

    Proceedings of the 54th ACM Symposium on Theory of Computing (STOC 2022)     page: 19 - 32   2022

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.1145/3519935.3519991

    Other Link: https://dblp.uni-trier.de/db/conf/stoc/stoc2022.html#GharibianG22

  3. Distributed Quantum Proofs for Replicated Data. Reviewed

    Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, Ami Paz

    Proceedings of the 12th Innovations in Theoretical Computer Science conference (ITCS 2021)     page: 28 - 20   2021

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ITCS.2021.28

    Other Link: https://dblp.uni-trier.de/db/conf/innovations/innovations2021.html#FraigniaudGNP21

  4. Tight Distributed Listing of Cliques. Reviewed

    Keren Censor-Hillel, Yi-Jun Chang, François Le Gall, Dean Leitersdorf

    Proceedings of the 32nd ACM-SIAM Symposium on Discrete Algorithms (SODA 2021)     page: 2878 - 2891   2021

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.1137/1.9781611976465.171

    Other Link: https://dblp.uni-trier.de/db/conf/soda/soda2021.html#Censor-HillelCG21

  5. Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture. Reviewed

    Sevag Gharibian, François Le Gall

    SIAM Journal on Computing   Vol. 52 ( 4 ) page: 1009 - 1038   2023.8

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    Publishing type:Research paper (scientific journal)  

    DOI: 10.1137/22m1513721

    Other Link: https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp52.html#GharibianG23

  6. Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems. Reviewed

    François Le Gall, Saeed Seddighin

    Algorithmica   Vol. 85 ( 5 ) page: 1251 - 1286   2023.5

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    Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00453-022-01066-z

  7. Distributed Quantum Interactive Proofs. Reviewed

    François Le Gall, Masayuki Miyamoto, Harumichi Nishimura

    Proceedings of the 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)     page: 42:1 - 42:21   2023

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.STACS.2023.42

    Other Link: https://dblp.uni-trier.de/db/conf/stacs/stacs2023.html#GallMN23

  8. Improved Hardness Results for the Guided Local Hamiltonian Problem. Reviewed

    Chris Cade, Marten Folkertsma, Sevag Gharibian, Ryu Hayakawa, François Le Gall, Tomoyuki Morimae, Jordi Weggemans

    Proceedings of the 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP 2023)     page: 32:1 - 32:19   2023

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ICALP.2023.32

    Other Link: https://dblp.uni-trier.de/db/conf/icalp/icalp2023.html#CadeFGHGMW23

  9. Quantum Distributed Computing: Potential and Limitations (Invited Talk).

    François Le Gall

    OPODIS     page: 2 - 1   2023

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.OPODIS.2023.2

    Other Link: https://dblp.uni-trier.de/db/conf/opodis/opodis2023.html#Gall23

  10. Quantum Distributed Algorithms for Detection of Cliques. Reviewed

    Keren Censor-Hillel, Orr Fischer, François Le Gall, Dean Leitersdorf, Rotem Oshman

    Proceedings of the 13th Innovations in Theoretical Computer Science conference (ITCS 2022)     page: 35 - 25   2022

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ITCS.2022.35

    Other Link: https://dblp.uni-trier.de/db/conf/innovations/innovations2022.html#Censor-HillelFG22

  11. Quantum Meets Fine-Grained Complexity: Sublinear Time Quantum Algorithms for String Problems. Reviewed

    François Le Gall, Saeed Seddighin

    Proceedings of the 13th Innovations in Theoretical Computer Science conference (ITCS 2022)     page: 97 - 23   2022

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ITCS.2022.97

    Other Link: https://dblp.uni-trier.de/db/conf/innovations/innovations2022.html#GallS22

  12. Quantum approximate counting for Markov chains and collision counting. Reviewed

    Francois Le Gall, Iu-Iong Ng

    Quantum Information & Computation   Vol. 22 ( 15&16 ) page: 1261 - 1279   2022

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    Publishing type:Research paper (scientific journal)  

    DOI: 10.26421/QIC22.15-16-1

  13. An Optimal Oracle Separation of Classical and Quantum Hybrid Schemes. Reviewed

    Atsuya Hasegawa, François Le Gall

    Proceedings of the 33rd International Symposium on Algorithms and Computation (ISAAC 2022)     page: 6 - 14   2022

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ISAAC.2022.6

    Other Link: https://dblp.uni-trier.de/db/conf/isaac/isaac2022.html#HasegawaG22

  14. Bounds on Oblivious Multiparty Quantum Communication Complexity. Reviewed

    François Le Gall, Daiki Suruga

    Proceedings of the 15th Latin American Theoretical Informatics Symposium (LATIN 2022)     page: 641 - 657   2022

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.1007/978-3-031-20624-5_39

    Other Link: https://dblp.uni-trier.de/db/conf/latin/latin2022.html#GallS22

  15. Brief Announcement: Distributed Quantum Interactive Proofs. Reviewed

    François Le Gall, Masayuki Miyamoto, Harumichi Nishimura

    Proceedings of the 36th International Symposium on Distributed Computing (DISC 2022)     page: 48 - 3   2022

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.DISC.2022.48

    Other Link: https://dblp.uni-trier.de/db/conf/wdag/disc2022.html#GallMN22

  16. Quantum Logarithmic Space and Post-Selection. Reviewed

    François Le Gall, Harumichi Nishimura, Abuzer Yakaryilmaz

    Proceedings of the 16th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2021)     page: 10 - 17   2021

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.TQC.2021.10

    Other Link: https://dblp.uni-trier.de/db/conf/tqc/tqc2021.html#GallNY21

  17. Test of Quantumness with Small-Depth Quantum Circuits. Reviewed

    Shuichi Hirahara, François Le Gall

    Proceedings of the 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)     page: 59 - 15   2021

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.MFCS.2021.59

    Other Link: https://dblp.uni-trier.de/db/conf/mfcs/mfcs2021.html#HiraharaG21

  18. Quantum communication complexity of distribution testing. Reviewed

    Aleksandrs Belovs, Arturo Castellanos, Francois Le Gall, Guillaume Malod, Alexander A. Sherstov

    Quantum Information & Computation   Vol. 21 ( 15&16 ) page: 1261 - 1273   2021

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.26421/QIC21.15-16-1

  19. Quantum Advantage with Shallow Circuits Under Arbitrary Corruption. Reviewed

    Atsuya Hasegawa, François Le Gall

    Proceedings of the 32nd International Symposium on Algorithms and Computation (ISAAC 2021)     page: 74 - 16   2021

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ISAAC.2021.74

    Other Link: https://dblp.uni-trier.de/db/conf/isaac/isaac2021.html#HasegawaG21

  20. Lower Bounds for Induced Cycle Detection in Distributed Computing. Reviewed

    François Le Gall, Masayuki Miyamoto

    Proceedings of the 32nd International Symposium on Algorithms and Computation (ISAAC 2021)     page: 58 - 19   2021

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.ISAAC.2021.58

    Other Link: https://dblp.uni-trier.de/db/conf/isaac/isaac2021.html#GallM21

  21. Quantum Distributed Algorithm for Triangle Finding in the CONGEST Model. Reviewed

    Taisuke Izumi, François Le Gall, Frédéric Magniez

    37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)   Vol. 154   page: 23 - 13   2020

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    Language:English   Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.STACS.2020.23

    Web of Science

    Other Link: https://dblp.uni-trier.de/db/conf/stacs/stacs2020.html#IzumiGM20

  22. Barriers for Rectangular Matrix Multiplication.

    Matthias Christandl, François Le Gall, Vladimir Lysikov, Jeroen Zuiddam

    Electron. Colloquium Comput. Complex.   Vol. 27   page: 30 - 30   2020

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    Publishing type:Research paper (scientific journal)  

    Other Link: https://dblp.uni-trier.de/db/journals/eccc/eccc27.html#ChristandlGLZ20

  23. Quantum-Inspired Classical Algorithms for Singular Value Transformation. Reviewed

    Dhawal Jethwani, François Le Gall, Sanjay K. Singh

    Proceedings of the 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)     page: 53 - 14   2020

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.MFCS.2020.53

    Other Link: https://dblp.uni-trier.de/db/conf/mfcs/mfcs2020.html#JethwaniGS20

  24. Quantum Speedup for the Minimum Steiner Tree Problem. Reviewed

    Masayuki Miyamoto, Masakazu Iwamura, Koichi Kise, François Le Gall

    Proceedings of the 26th International Computing and Combinatorics Conference (COCOON 2020)     page: 234 - 245   2020

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.1007/978-3-030-58150-3_19

    Other Link: https://dblp.uni-trier.de/db/conf/cocoon/cocoon2020.html#MiyamotoIKG20

  25. On Distributed Listing of Cliques. Reviewed

    Keren Censor-Hillel, François Le Gall, Dean Leitersdorf

    Proceedings of the 39th ACM Symposium on Principles of Distributed Computing (PODC 2020)     page: 474 - 482   2020

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.1145/3382734.3405742

    Other Link: https://dblp.uni-trier.de/db/conf/podc/podc2020.html#Censor-HillelGL20

  26. Fast Distributed Algorithms for Girth, Cycles and Small Subgraphs. Reviewed

    Keren Censor-Hillel, Orr Fischer, Tzlil Gonen, François Le Gall, Dean Leitersdorf, Rotem Oshman

    Proceedings of the 34th International Symposium on Distributed Computing (DISC 2020)     page: 33 - 17   2020

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.DISC.2020.33

    Other Link: https://dblp.uni-trier.de/db/conf/wdag/disc2020.html#Censor-HillelFG20

  27. Brief Announcement: Distributed Quantum Proofs for Replicated Data. Reviewed

    Pierre Fraigniaud, François Le Gall, Harumichi Nishimura, Ami Paz

    Proceedings of the International Symposium on Distributed Computing (DISC 2020)     page: 43 - 3   2020

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    Publishing type:Research paper (international conference proceedings)  

    DOI: 10.4230/LIPIcs.DISC.2020.43

    Other Link: https://dblp.uni-trier.de/db/conf/wdag/disc2020.html#FraigniaudGNP20

  28. Finding Small and Large $k$-Clique Instances on a Quantum Computer Reviewed

    Sara Ayman Metwalli, Francois Le Gall, Rodney Van Meter

    IEEE Transactions on Quantum Engineering   Vol. 1   page: 1 - 11   2020

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    Publishing type:Research paper (scientific journal)   Publisher:Institute of Electrical and Electronics Engineers (IEEE)  

    DOI: 10.1109/tqe.2020.3045692

  29. Average-Case Quantum Advantage with Shallow Circuits. Reviewed

    François Le Gall

    34th Computational Complexity Conference, CCC 2019, July 18-20, 2019, New Brunswick, NJ, USA.     page: 21:1-21:20   2019

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    Publisher:Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik  

  30. Quantum Advantage for the LOCAL Model in Distributed Computing

    Le Gall Francois, Nishimura Harumichi, Rosmanis Ansis

    36TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE (STACS 2019)     2019

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  31. Generalized Quantum Arthur-Merlin Games. Reviewed

    Hirotada Kobayashi, François Le Gall, Harumichi Nishimura

    SIAM J. Comput.   Vol. 48 ( 3 ) page: 865 - 902   2019

  32. Quantum Advantage for the LOCAL Model in Distributed Computing. Reviewed

    François Le Gall, Ansis Rosmanis, Harumichi Nishimura

    36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019, March 13-16, 2019, Berlin, Germany     page: 49:1-49:14   2019

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    Publisher:Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik  

  33. Quantum Query Complexity of Unitary Operator Discrimination. Reviewed

    Akinori Kawachi, Kenichi Kawano, Francois Le Gall, Suguru Tamaki

    IEICE Transactions   Vol. 102-D ( 3 ) page: 483 - 491   2019

  34. Quantum Distributed Algorithm for the All-Pairs Shortest Path Problem in the CONGEST-CLIQUE Model. Reviewed

    Taisuke Izumi, François Le Gall

    Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, ON, Canada, July 29 - August 2, 2019.     page: 84 - 93   2019

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    Publisher:ACM  

    DOI: 10.1145/3293611.3331628

  35. Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups. Reviewed

    François Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi

    43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, August 27-31, 2018, Liverpool, UK     page: 26:1-26:13   2018

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    Publisher:Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik  

    DOI: 10.4230/LIPIcs.MFCS.2018.26

  36. Improved rectangular matrix multiplication using powers of the coppersmith-winograd tensor Reviewed

    François Le Gall, Florent Urrutia

    Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms     page: 1029 - 1046   2018

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Association for Computing Machinery  

    In the past few years, successive improvements of the asymptotic complexity of square matrix multiplication have been obtained by developing novel methods to analyze the powers of the Coppersmith-Winograd tensor, a basic construction introduced thirty years ago. In this paper we show how to generalize this approach to make progress on the complexity of rectangular matrix multiplication as well, by developing a framework to analyze powers of tensors in an asymmetric way. By applying this methodology to the fourth power of the Coppersmith-Winograd tensor, we succeed in improving the complexity of rectangular matrix multiplication. Let denote the maximum value such that the product of an n n matrix by an n n matrix can be computed with O(n2+) arithmetic operations for any &gt
    0. By analyzing the fourth power of the Coppersmith-Winograd tensor using our methods, we obtain the new lower bound &gt
    0:31389, which improves the previous lower bound &gt
    0:30298 obtained by Le Gall (FOCS'12) from the analysis of the second power of the Coppersmith-Winograd tensor. More generally, we give faster algorithms computing the product of an n nk matrix by an nk n matrix for any value k 6= 1. (In the case k = 1, we recover the bounds recently obtained for square matrix multiplication). These improvements immediately lead to improvements in the complexity of a multitude of fundamental problems for which the bottleneck is rectangular matrix multiplication, such as computing the all-pair shortest paths in directed graphs with bounded weights.

    DOI: 10.1137/1.9781611975031.67

    Scopus

  37. Sublinear-Time Quantum Computation of the Diameter in CONGEST Networks. Reviewed

    François Le Gall, Frédéric Magniez

    Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, July 23-27, 2018     page: 337 - 346   2018

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  38. Quantum Algorithm for Triangle Finding in Sparse Graphs Reviewed

    Francois Le Gall, Shogo Nakajima

    ALGORITHMICA   Vol. 79 ( 3 ) page: 941 - 959   2017.11

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. (SIAM J Comput 34(6):1324-1330, 2005). Our algorithm is based on the recent (O) over tilde (n(5/4))-query algorithm given by Le Gall (Proceedings of the 55th IEEE annual symposium on foundations of computer science, pp 216-225, 2014) for triangle finding over dense graphs (here n denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with O(n(5/4-epsilon)) queries for some constant epsilon > 0 whenever the graph has at most O(n(2-c))edges for some constant c > 0.

    DOI: 10.1007/s00453-016-0267-z

    Web of Science

  39. MODIFIED GROUP NON-MEMBERSHIP IS IN PROMISE-AWPP RELATIVE TO GROUP ORACLES Reviewed

    Tomoyuki Morimae, Harumichi Nishimura, Francois Le Gall

    QUANTUM INFORMATION & COMPUTATION   Vol. 17 ( 3-4 ) page: 242 - 250   2017.3

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:RINTON PRESS, INC  

    It is known that the group non-membership problem is in QMA relative to any group oracle and in SPPnBQP for solvable groups. We consider a modified version of the group non-membership problem where the order of the group is also given as an additional input. We show that the problem is in (the promise version of) AWPP relative to any group oracle. To show the result, we use the idea of postselected quantum computing.

    Web of Science

    Other Link: http://dblp.uni-trier.de/db/journals/qic/qic17.html#journals/qic/MorimaeNG17

  40. Probabilistic Logarithmic-Space Algorithms for Laplacian Solvers. Reviewed

    Dean Doron, François Le Gall, Amnon Ta-Shma

    Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2017, August 16-18, 2017, Berkeley, CA, USA     page: 41:1-41:20   2017

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    Publisher:Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik  

    DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.41

  41. Multiparty Quantum Communication Complexity of Triangle Finding. Reviewed

    François Le Gall, Shogo Nakajima

    12th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2017, June 14-16, 2017, Paris, France     page: 6:1-6:11   2017

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    Publisher:Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik  

    DOI: 10.4230/LIPIcs.TQC.2017.6

  42. Quantum Algorithms for Matrix Products over Semirings. Reviewed

    François Le Gall, Harumichi Nishimura

    Chicago J. Theor. Comput. Sci.   Vol. 2017   2017

  43. Triangle Finding and Listing in CONGEST Networks. Reviewed

    Taisuke Izumi, François Le Gall

    Proceedings of the ACM Symposium on Principles of Distributed Computing, PODC 2017, Washington, DC, USA, July 25-27, 2017     page: 381 - 389   2017

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  44. Quantum query complexity of unitary operator discrimination Reviewed

    Akinori Kawachi, Kenichi Kawano, François Le Gall, Suguru Tamaki

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   Vol. 10392   page: 309 - 320   2017

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer Verlag  

    Unitary operator discrimination is a fundamental problem in quantum information theory. The basic version of this problem can be described as follows: given a black box implementing a quantum the promise that the black box implements either the unitary operator U:1 or the unitary operator U:2, the goal is to decide whether U=U:1 or U=U:2. In this paper, we consider the query complexity of this problem. We show that there exists a quantum algorithm that solves this problem with bounded-error probability using (formula presented) \\right\\rceil queries to the black-box, where \\theta _\\mathrm{cover} represents the “closeness” between U:1 and U:2 (this parameter is determined by the eigenvalues of the matrix (formula presented). We also show that this upper bound is essentially tight: we prove that there exist operators U:1 and U:2 such that any quantum algorithm solving this problem with bounded-error probability requires at least (formula presented) queries.

    DOI: 10.1007/978-3-319-62389-4_26

    Scopus

▼display all

Presentations 13

  1. Quantum distributed computing: potential and limitations Invited

    Le Gall Francois

    2023 CONFERENCE ON PRINCIPLES OF DISTRIBUTED SYSTEMS (OPODIS 2023)  2023.12.7 

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    Event date: 2023.12

    Presentation type:Oral presentation (invited, special)  

  2. Quantum Algorithms: Applications and Theoretical Foundations Invited

    Francois Le Gall

    The 13 th International Symposium for Sustainability by Engineering at Mie University (Research Area C)  2023.11.22 

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    Event date: 2023.11

    Language:English   Presentation type:Oral presentation (invited, special)  

  3. Theoretical Foundations of Quantum Advantage in Quantum Computing Invited

    Francois Le Gall

    京都大学基礎物理学研究所 創立70周年記念シンポジウム  2023.11.22 

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    Event date: 2023.11

    Presentation type:Oral presentation (invited, special)  

  4. Theoretical Foundations of Quantum Advantage for Quantum Algorithms Invited

    Francois Le Gall

    YIPQS long-term workshop Quantum Information, Quantum Matter and Quantum Gravity  2023.9.20 

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    Event date: 2023.9

    Presentation type:Oral presentation (invited, special)  

  5. 多人数の量子通信複雑性における新しい手法

    第47回量子情報技術研究会  2022.12.8 

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    Event date: 2022.12

  6. Distributed Merlin-Arthur Synthesis of Quantum States and Its Applications

    第47回量子情報技術研究会  2022.12.8 

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    Event date: 2022.12

  7. ガイド付きローカルハミルトニアン問題の計算複雑性の進展

    第47回量子情報技術研究会  2022.12.8 

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    Event date: 2022.12

  8. Quantum Distributed Computing Invited

    Workshop on Advances in Distributed Graph Algorithms (ADGA 2022)  2022.10.24 

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    Event date: 2022.10

  9. Theoretical Foundations of Quantum Advantage Invited

    Q2B 2022 Tokyo  2022.7.14 

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    Event date: 2022.7

  10. 分散量子対話型証明

    第6回量子ソフトウェア研究会  2022.7.8 

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    Event date: 2022.7

  11. Bounds on oblivious multiparty quantum communication complexity

    第6回量子ソフトウェア研究会  2022.7.8 

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    Event date: 2022.7

  12. Quantum algorithms for large-scale problems Invited International conference

    François Le Gall

    Quantum Innovation 2021, the International Symposium on Quantum Science, Technology and Innovation  2021.12.9 

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    Event date: 2021.12

    Language:English   Presentation type:Oral presentation (invited, special)  

  13. Tight Distributed Listing of Cliques Invited

    2021.3.8 

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    Event date: 2021.3

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KAKENHI (Grants-in-Aid for Scientific Research) 9

  1. 中規模量子コンピュータによるセキュアな分散型量子計算の基盤創出

    Grant number:24H00071  2024.4 - 2029.3

    科学研究費助成事業  基盤研究(S)

    ルガル フランソワ

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    Authorship:Principal investigator 

    Grant amount:\203450000 ( Direct Cost: \156500000 、 Indirect Cost:\46950000 )

  2. Quantum Algorithms for Large-Scale Quantum Computers: New Horizons and Applications International coauthorship

    Grant number:20H04139  2020.4 - 2024.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\17290000 ( Direct Cost: \13300000 、 Indirect Cost:\3990000 )

  3. Algebraic Complexity Theory: New Approaches and Algorithmic Applications International coauthorship

    Grant number:16H05853  2016.4 - 2020.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Young Scientists (A)

    Le Gall Francois

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\12480000 ( Direct Cost: \9600000 、 Indirect Cost:\2880000 )

    In this research project we developed new techniques based on algebraic complexity theory to solve problems from theoretical computer science. Our main achievements are as follows.
    We first developed new approaches to solve algebraic problems, and constructed faster algorithms for rectangular matrix multiplication. We then showed how to apply in a novel way algebraic techniques to several problems from computer science. In particular, via this approach we designed fast distributed algorithms for various computational problems over networks. Finally, we designed several quantum algorithms for graph problems that are faster than the best known algorithms.

  4. Construction of Quantum Computaional Infrastracture towards Quantum Information Society International coauthorship

    Grant number:21H04879  2021.4 - 2026.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

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    Authorship:Coinvestigator(s)  Grant type:Competitive

  5. 量子アルゴリズムの理論と実装を接続する革新的基盤の創出

    Grant number:20H05966  2020.11 - 2025.3

    科学研究費助成事業  学術変革領域研究(A)

    山下 茂, 山本 直樹, ルガル フランソワ, 森 立平, 谷 誠一郎, 西村 治道

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    Authorship:Coinvestigator(s) 

    量子計算各種モデルにおける計算能力の解析を行う理論的なアプローチと、実際に量子計算機を利用する実践的なアプローチの両面から以下の4項目の研究を行う。
    (A) 既存の量子計算モデルの結果を量子・古典協調の観点から、あるいは「弱い」量子計算モデルの観点から再検討・再構築する。
    (B) 量子計算に起こりうる現実的なエラーを考慮に入れた計算モデルの検討を進める。
    (C) 量子計算の方式に応じて異なる量子回路のモデルを量子・古典協調利用の枠組みの中で検討・評価する。
    (D) 量子計算と古典計算を協調して利用する計算アルゴリズムの能力を解析するための計算モデルを検討・評価する。

  6. 量子アルゴリズム・計算量・浅層回路と量子コンピュータ実機実験による量子優位性研究 International coauthorship

    Grant number:20H00579  2020.4 - 2025.3

    日本学術振興会  科学研究費助成事業  基盤研究(A)

    今井 浩, 山下 茂, ルガル フランソワ, Avis David

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    Authorship:Coinvestigator(s)  Grant type:Competitive

    量子コンピュータの得意な問題を用いて量子計算優越性を達成したとGoogleの研究者らが主張したところである。しかし、その問題は実応用とは無縁であり、IT社会に多大なインパクトを与えるの量子素因数分解計算などの実機実装の研究が重要となっている。本研究では、量子計算が本研究グループの量子浅層回路の計算量理論・実機に対応する量子回路の設計理論・量子非局所性とその組み合わせ構造に着目することにより、理論的に真に高速と示すことができる量子優位性を有する問題の最先端を研究し、量子コンピュータ実機で実証する。このような取り組みで、量子優位性が直接的に実社会に影響を与える新たな問題群を見出す成果を目指す。
    2年度目の研究では、IBMの65量子ビットの量子コンピュータが研究代表者のところで利用できるようになり、それを用いて量子グラフ状態の一般化Bell不等式の破れの研究を進めることができた。65量子ビットのレベルでは、古典シミュレーションもかなり難しくなるとともに、それまでのエラー緩和手法が量子ビット数の指数時間かかっていた点が大きな問題として顕在化する。それを解決するための研究を進め、新たに100量子ビットレベルでも適用できる測定エラーに対するエラー緩和法を提案した。これは初年度に見出した課題を解決したものである。これを次年度に続けて、論文として公開するに至っている。浅層回路に関する計算量理論からの解析では、定数段から次のステップとして、量子ビット数の対数深さのものを考え、それについて取り組みを始めた。この問題の周辺には、Jozsaの予想という浅層回路を古典計算とハイブリッドで用いた場合の計算量に関する問題と密に関係しており、その回目に向けて明確な一歩を次年度に国際会議で論文を成果発表すること示した。分担者のLe Gallは、量子分散計算に関して自ら構築した枠組みの中で活発な研究を進め、国際会議で発表するとともに、研究コミュニティのリーダとして国際会議のプログラム策定などで貢献もしている。分担者の山下が中心となって研究を進め、実機への応用を目指した回路設計の研究も始めており、Sゲートを用いてTゲート・Toffliゲートの数を改善する量子回路設計法や、SATを用いた設計論を展開した。分担者のAvisがスタートさせた量子重力理論の共形場でのエントロピー錐の研究を凸多面体解析を自ら開発した並列プログラムで解析するなどして、次年度に論文発表することにつながっている。
    初年度は研究の中で、新たに量子計算の範囲を拡大する研究課題を設定することができ、2年度でそれらの成果創出に向けて取り組んだ。まだコロナ禍の影響があり、海外研究者の招へいは難しいところであるが、次年度にそれを実現して研究推進する展開も検討した。
    <BR>
    量子コンピュータ実機利用では、65量子ビットの量子コンピュータがさらに127量子ビットのものも利用が始まり、一般化Bell不等式を用いた浅層回路をベンチマーク的に利用することも可能となった。浅層回路の計算量理論・回路設計論の観点からの研究も進展しており、おおむね順調に研究が進展していると判断している。
    2年度目の研究を通して、当初目標を拡張した研究計画に沿って、さらに研究推進していく。その中で、エントロピー錐を量子計算的に理解する研究も進める。浅層回路については対数深さの回路独自に解ける問題とともに、それを古典計算とハイブリッド計算した場合の研究をスタートさせる。量子回路設計理論についても、将来の量子誤り訂正実現の観点からの研究に取り組む。

  7. Theoretical Research on Quantum Supremacy

    Grant number:19F19079  2019.7 - 2021.3

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    Authorship:Other 

  8. 対話型証明の新展開-古典から量子まで

    Grant number:19H04066  2019.4 - 2023.3

    科学研究費助成事業  基盤研究(B)

    西村 治道, ルガル フランソワ, 森前 智行, Buscemi F.

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    Authorship:Coinvestigator(s) 

    今日の量子計算量理論において,対話型証明の概念は非常に大きな存在となっている.一方で,近年その実装へ向けて社会的注目を集める量子コンピュータはまだ小規模であり,量子メモリや量子通信は依然として高コストである.この状況を鑑みて,本研究では量子計算や量子通信が制限された量子対話型証明や量子計算に動機づけられた古典対話型証明,さらにはその中間的な対話型証明モデルに着目し,それらの対話型証明モデルについての計算量理論を展開する.これにより量子コンピュータの検証問題に対する新しい解決法を提案し,既存の量子対話型証明モデルや量子多項式階層理論を俯瞰的に捉えることができるような包括的成果を得ることを目指す.

  9. Interpolative Expansion of Quantum Protocol Theory International coauthorship

    Grant number:16H01705  2016.4 - 2021.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

    Takeshi Koshiba

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    Authorship:Coinvestigator(s)  Grant type:Competitive

    The computational power of the DQC1 model, which is a formalization of non-universal quantum computation with initialization-hard quantum states, is shown to be superior to classical computation. Many quantum distributed algorithms are developed. Under the standard model for distributed algorithms, efficient quantum protocols for several fundamental problems such as the shortest path problem. Secure quantum delegated computation cannot achieve the perfect security for classical clients. By introducing the notion of rewards in quantum computations, classical verification of having the quantum power of the server is affirmatively settled. This is a game-theoretic solution and gives a novel method in quantum computation.

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